The length of the garden is 63 feet and the width is 42 feet.
Explanation:Let's assume that the length of the garden is x feet. According to the problem, the width is two-thirds of the length, so the width is (2/3)x feet.
The perimeter of a rectangle is given by the formula P = 2(l+w), where P is the perimeter, l is the length, and w is the width. In this case, the perimeter is 210 feet, so we have the equation 210 = 2(x + (2/3)x).
Simplifying the equation, we get 210 = 2(5/3)x. By dividing both sides by 2, we find that (5/3)x = 105. Finally, solving for x, we get x = 105 * (3/5) = 63 feet. Therefore, the length of the garden is 63 feet, and the width is (2/3) * 63 = 42 feet.
What's the circumference of a circle with a diameter of 30 cm
In the marching band at Hometown High, there are 77 woodwinds and 88 brass. If there is an equal number of woodwind and brass musicians in each row, what is the greatest number of rows in a performance? A) 9 rows B) 11 rows C) 13 rows D) 15 rows
the back of a moving truck is 4 feet above the ground. A ramp extending from the back of the truck meets the ground 10 feet from the truck. What is the slope of the ramp?
Answer:
20 feet
Step-by-step explanation:
Jana Has $5. She wants to buy a notebook for $4.50.The sales tax is 7%. Does she have enough money? Explain your reasoning.
Two well-known aviation training schools are being compared using random samples of their graduates. it is found that 70 of 140 graduates of fly-more academy passed their faa exams on the first try, compared with 104 of 260 graduates of blue yonder institute. in a two-tailed test, the p-value is .0275, so at = .025 we should:
Final answer:
With a p-value of .0275 being greater than the significance level of .025, the decision in a two-tailed test would be to not reject the null hypothesis, indicating insufficient evidence to show a significant difference between the two schools' FAA exam pass rates.
Explanation:
The student is given information about the performance of the graduates from two aviation training schools regarding FAA exam pass rates on the first try. The pass rates are compared using a statistical hypothesis test, and the p-value from this test is .0275. When the level of significance (α) is set at .025, and we are conducting a two-tailed test, we should make a decision about whether to reject or not reject the null hypothesis.
Since the p-value (.0275) is greater than the level of significance (α = .025), the correct decision would be not to reject the null hypothesis. It means that there's not enough statistical evidence to show a significant difference between the FAA exam pass rates of the two schools at the .025 level of significance. This matches the general hypothesis testing rule: if the p-value is less than α, reject the null hypothesis; otherwise, do not reject it.
In the fiscal year of 1991-1992, a total of 109,782 child labor permits were issued, 2/3 of which were males. The monthly average for males is?
Final answer:
The monthly average for males who received child labor permits in the fiscal year of 1991-1992 is approximately 6,099, calculated by multiplying the total permits (109,782) by 2/3 and then dividing by 12 months.
Explanation:
To calculate the monthly average for males who received child labor permits in the fiscal year of 1991-1992, we first determine the total number of permits issued to males. Since 2/3 of the total permits were issued to males, we multiply the total number of permits, 109,782, by 2/3:
Total permits for males = 109,782 * (2/3) = 73,188
There are 12 months in a fiscal year, so to find the monthly average, we divide the total permits for males by 12:
Monthly average for males = 73,188 / 12 ≈ 6,099
Therefore, the monthly average number of child labor permits issued to males was approximately 6,099.
Gerard bought 9 hamburgers and 3 orders of fries for 24.75. Chris bought 6 hamburgers and 4 orders of fries for 19.50. Each hamburger cost the same amount. Each Order of fries cost the same amount. Wrote a system of equations that can be used to find how much one hamburger and one Order of fries cost.
Answer:
System of equations:
9x+3y=24.75
6x+4y=19.50
x: cost of a hamburger
y: cost of an order of fries
Step-by-step explanation:
We define the variables of the system of equations:
x: cost of a hamburger
y: cost of an order of fries
We propose the system of equations:
To Gerard: 9x+3y=24.75
To Chris: 6x+4y=19.50
where, the coefficients in the equations represent the quantity that was purchased from each product and the variables represent the costs of each product.
write 91.4 million in both standard form and in scientific notation
91.4 million in standard form is 91400,000.
To express 91.4 million in standard form,
We simply write the number as it is: 91,400,000.
In this form, each place value is clearly represented by its corresponding digit.
In scientific notation, we express the number as a product of a decimal number between 1 and 10, multiplied by a power of 10. For 91.4 million,
It can be written as 9.14 x 10⁷.
In this notation, the decimal point is placed after the first digit, and the power of 10 represents the number of places the decimal point should be moved to the right to obtain the original value.
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Find the partial derivatives of the function w=4r2+6s2+
Fred lives in Syler City, where the tax rate is 3.5%. His property is assessed at $93,000. What is his tax?
PLEASE HELP!!! WILL BRAINLIEST
Jane ran 3/8 of the distance that Jack ran. If Jane ran 2/3 of a mile, how far did Jack run?
Which of these could be used to solve the problem?
A. 3/8 * = 2/3
B. 2/3 * = 3/8
C. x=(2/3) (3/8)
D. x=3/8 *- 2/3*
Using proportions, it is found that the distance that Jack ran is given by:
A. [tex]\frac{3}{8}x = \frac{2}{3}[/tex]
The distance ran by Jane was of [tex]\frac{2}{3}[/tex] of a mile.This distance was also [tex]\frac{3}{8}[/tex] of the distance ran by Jack, which is given by x.Applying the proportion, we have that [tex]\frac{3}{8}[/tex] multiplied by x is equals to [tex]\frac{2}{3}[/tex], hence:
[tex]\frac{3}{8}x = \frac{2}{3}[/tex]
Which means that the correct option is given by a.
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If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 36 inches, what diameter pizza will reward you with the largest slice? in
We start by expressing the circumference and the size of the slice in terms of the pizza's radius. By setting the pizza slice to be the largest (having an angle of 2π at the centre), we find the radius and hence the diameter of the pizza.
Explanation:The question falls into the area of Circle Geometry. Let's say the radius of the pizza is r inches, the length of the crust is a, and the length of the two straight edges of the pizza slice (each of which is a radius of the circle) are both r.
According to the problem, the perimeter of the pizza slice is given as 36 inches. This sums up the two radii and the length of the crust (a). Therefore, 2r + a = 36.
We know that the crust's length is a fraction of the total circumference of the circle. The whole circle's perimeter is 2πr.
Assuming the angle at the center of the pizza slice is θ (in radians), we have a = θr. θ will be a fraction of 2π depending on the size of the slice.
Substituting θr for a in the equation 2r + a = 36, we get 2r + θr = 36. To get the largest slice, θ has to be as large as possible, 2π.
Replace θ with 2π, we have 2r + 2πr = 36. Solve for r and we find that r = 36/(2+2π). That gives the radius of the pizza. Multiply r by 2 will give us the diameter of the pizza.
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After entering the test scores from her statistics class of 25 students, the instructor calculated the mean and the median of the scores. upon checking, she discovered that the toptop score entered was 73, but it should have been 83. when she corrects this score, how will the mean and median be affected?
what is the volume of a tank that can hold 18 754 Kg of methanol whose density is 0.788g/cm3
The volume of a tank is 23.8m3
that can hold 18 754 Kg of methanol whose density is 0.788g/cm3
Using this formula
Volume=m/p
Let plug in the formula
Volume=18,754 kg/0.788g/cm3
Volume=18,754,000g/0.788g/cm3
Volume=23,799,4924cm2
Volume=23.8m3 (Approximately)
Inconclusion The volume of a tank is 23.8m3.
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A doctor's office has a computer file showing the heights of 100 male patients of one of the doctors of the practice. the heights range from 18 inches to 68 inches. by accident, the greatest height has been recorded as 680 inches, instead of 68 inches. (a) does this affect the average? if so, by how much? (b) does this affect the median? if so by how much?
The effect of the mistake is:
The mean value obtained is larger. The median value is not affected.The average value recorded is larger than it actually is. Hence , the average value is affected by the mistake. Given the information supplied, we can only deduce that the mean value will be greater than the actual average.
The mean involves taking the sum of all the values and dividing it by the number of values.
Using a value of 680 instead of 68 will mean that, the sum obtained is greater than the actual sum.
The median on the other hand isn't affected by this error, because, the arrangement of the values isn't changed.
The sorting of values is very crucial to calculating the Median. However, either 68 or 680. The position of the maximum value remains unchanged.
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A School raised $13,809 during it's fall fundraiser and $20,786 during it's winter fundraiser. The total fundraising goal for the school year is $50,000. How much more money does the school need to raise during the spring fundraiser to reach its goal?
Show your work...
The extra fundraiser school should get is $15405.
What is a fundraiser?A fundraiser is an event which is intended to raise money for a particular purpose, for example, for a charity.
Given that, A School raised $13,809 during its fall fundraiser and $20,786 during its winter fundraiser. The total fundraising goal for the school year is $50,000.
The yet total fundraised = fall fundraiser + winter fundraiser
= $13,809 + $20,786
= $34595
Since, they need $50000 in total,
Therefore, remaining amount = total - collected
= $50000 - $34595
= $15405.
Hence, the extra fundraiser school should get is $15405.
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An arrow is shot vertically upward from a platform 25ft high at a rate of 172ft/sec. When will the arrow hit the ground?
choices are (mode, mean, median)
A sample was selected and the eye color of every person in the sample was recorded.
{Brown,Brown,Green,Blue,Brown,Green,Hazel,Brown,Green,Hazel}
The ___________ should be used.
A Girl Scout troop sold cookies. The number of boxes each scout sold is listed below.
{35,45,47,27,50,43,25,52,37,312}
The ___________ should be used.
A pizza parlor sold the follow number of pizzas each day from January 27-28.
{30,28,23,25,35,27,29}
The __________ should be used.
Jack wants to buy a skateboard that usually sells for $79.40. All merchandise is discounted by 12%. What is the total cost of the skateboard if Jack has to pay a state sales tax of 6.75%. Round your intermediate calculations and answer to the nearest cent.
the change in the x-coordinates of any two points on a line in the xy-plane is the
Answer
D the run. AP3X
Which of the following represents the vertical asymptotes of the function
what are partial products of 374 times 510
If a truck traveled 75.648 miles per year how many miles did it travel monthly
Order the fractions from least to greatest 5/8, 3/4, 1/2, 9/16
The Museum of Science in Boston has an exhibit in which metal balls drop down a chute, bounce around, and wind up in one of 21 bins. After 1000 balls have dropped, the heights within the bins clearly follow a bell-shaped curve. The standard deviation is 3 bins.
About how many balls are in bins 1 through 17?
Using the Empirical Rule, we can estimate that about 95% of the balls (950 balls) will fall within the first 17 bins of the bell-shaped distribution, with a standard deviation of 3 bins.
To determine how many balls are in bins 1 through 17 at the Museum of Science in Boston, we can apply the Empirical Rule to the bell-shaped distribution of balls in bins.
Since we have a standard deviation of 3 bins, and a bell-shaped curve approximates a normal distribution, about 95% of the data (balls) will be within two standard deviations of the mean.
Assuming approximately equal distribution across the bins and a large number of trials, bins 1 through 17 would contain slightly less than 95% of the balls, as they represent less than two standard deviations from the mean.
Here is a rough estimate:
Total balls: 1000
Two standard deviations: 95% of 1000 balls = 950 balls
Bins 1 through 17 contain slightly less than 950 balls.
Without the exact mean, we cannot provide a precise number, but we can conclude that about 950 balls will be distributed in bins 1 through 17, give or take, based on the data provided and properties of the normal distribution.
if a debt of $480 is reduced by 20% find the new debt
To find the new debt after a 20% reduction, subtract 20% of the original debt from the original debt.
Explanation:To find the new debt after a 20% reduction, we need to subtract 20% of the original debt from the original debt. Here's how to calculate it:
Convert 20% into a decimal by dividing it by 100: 20% = 0.20Multiply 0.20 by $480 to find the reduction amount: 0.20 x $480 = $96Subtract $96 from $480 to find the new debt: $480 - $96 = $384Therefore, the new debt after a 20% reduction is $384.
The new debt after being reduced by 20% is $384.
Explanation:To find the new debt after it has been reduced by 20%, we can use the following steps:
Calculate 20% of $480 by multiplying 480 by 0.20. 20% of 480 is $96.Subtract the amount calculated in step 1 from the original debt. The new debt is $480 - $96 = $384Therefore, the new debt after being reduced by 20% is $384.
Joe completed 28 math problem from his homework. Joe has done 80% of his homework. How many more math problem does Joe have to complete
0% = 0.8
divide 28 by 0.8
28 / 0.8 = 35 total questions
35 -28 = 7 more questions to do
What is the value of x? Enter your answer in the box
using Pythagorean Theorem
x^2 +b^2 = c^2
x^2 +12^2 = 13^2
x^2 +144 = 169
x^2 = 25
x = sqrt(25) = 5
x = 5
What is the constant of proportionality for the ratios 2 to 3 and 4 to 6?
Answer:2/3
Step-by-step explanation:
−8x+4y=24
−7x+7y=28
What is the solution?